document.write( "Question 1025448: Heights of women have a​ bell-shaped distribution with a mean of 163cm and a standard deviation of 8cm. Using​ Chebyshev's theorem, what do we know about the percentage of women with heights that are within 3 standard deviations of the​mean? What are the minimum and maximum heights that are within 3 standard deviations of the​ mean? \n" ); document.write( "
Algebra.Com's Answer #640733 by robertb(5830)\"\" \"About 
You can put this solution on YOUR website!
Chebyshev's theorem states that in general for any distribution, \r
\n" ); document.write( "\n" ); document.write( "\"P%28abs%28X+-+mu%29%3C=k%2Asigma%29%3E=1-1%2Fk%5E2\".\r
\n" ); document.write( "\n" ); document.write( "==> \"P%28abs%28X+-+mu%29%3C=3%2Asigma%29%3E=1-1%2F3%5E2+=+1-1%2F9+=+8%2F9\", or AT LEAST 88.9% are within 3 standard deviations of the mean.\r
\n" ); document.write( "\n" ); document.write( "\"abs%28X+-+163%29%3C=3%2A8+=+24\" ==> \"-24+%3C=+X+-+163+%3C=24\"\r
\n" ); document.write( "\n" ); document.write( "==> \"139+%3C=+X+%3C=+187\"\r
\n" ); document.write( "\n" ); document.write( "==> the minimum and maximum heights that are within 3 standard deviations of the​ mean are 139 and 187, respectively.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );